Abstract
When designing any artificial beach, it’s desirable to avoid (or minimise) future maintenance commitments by arranging the initial beach planshape so that it remains in equilibrium given the incident wave climate. Headlands bays, or embayments, where a sandy beach is held between two erosion resistant headlands, tend to evolve to a stable beach planshape with little movement of the beach contours over time. Several empirical bay shape equations have been derived to fit curves to the shoreline of headland bay beaches. One of the most widely adopted empirical equations is the parabolic bay shape equation, as it is the only equation that directly links the shoreline positions to the predominant wave direction and the point of diffraction. However, the main limitation with the application of the parabolic bay shape equation is locating the downcoast control point. As a result of research presented in this paper a new equation, based on the hyperbolic tangent shape equation was developed, which eliminates the requirement of placing the down coast control point and relies on defining a minimum beach width instead. This modified equation was incorporated into a new ArcGIS tool.
Highlights
Rocky coasts with headland bay beaches represent about 50 % of the world’s coastline (Short and Masselink, 1999)
Case studies In order to overcome the major shortcoming of the hyperbolic tangent equation, a relationship linking the geometric origin of the hyperbolic tangent equation with a wave diffraction point needed to be determined
This led to the following relationships, which were used to identify the location of the coordinates of the wave diffraction point for the hyperbolic tangent equation: c/a 1.256 x for the coordinate d/a 0.517 for the y coordinate
Summary
Rocky coasts with headland bay beaches represent about 50 % of the world’s coastline (Short and Masselink, 1999). The origin of the equation, unlike the log spiral, is the wave diffraction point around the headland and the result is a beach planshape in static equilibrium. This makes the equation ideal for engineering purposes. In contrast to the log-spiral and the hyperbolic tangent shape equation, the parabolic bay shape equation links the change of the shoreline to the point of wave diffraction upcoast. The work reported here has set out to determine a relationship linking the existing hyperbolic tangent shape equation with the wave diffraction point and wave obliquity This would eliminate the ambiguity of locating the downcoast control point associated with the parabolic bay shape equation. The rest of this paper presents the methodology and application of the modified hyperbolic tangent bay shape equation
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